19.6: Difference between revisions

Latest revision as of 11:49, 28 June 2021

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
19.6#Ex1	${\displaystyle{\displaystyle K\left(0\right)=E\left(0\right)}}$ `\compellintKk@{0} = \compellintEk@{0}`		EllipticK(0) = EllipticE(0)	EllipticK[(0)^2] == EllipticE[(0)^2]	Successful	Successful	-	Successful [Tested: 1]
19.6#Ex1	${\displaystyle{\displaystyle E\left(0\right)={K^{\prime}}\left(1\right)}}$ `\compellintEk@{0} = \ccompellintKk@{1}`		EllipticE(0) = EllipticCK(1)	EllipticE[(0)^2] == EllipticK[1-(1)^2]	Successful	Successful	-	Successful [Tested: 1]
19.6#Ex1	${\displaystyle{\displaystyle{K^{\prime}}\left(1\right)={E^{\prime}}\left(1% \right)}}$ `\ccompellintKk@{1} = \ccompellintEk@{1}`		EllipticCK(1) = EllipticCE(1)	EllipticK[1-(1)^2] == EllipticE[1-(1)^2]	Successful	Successful	-	Successful [Tested: 1]
19.6#Ex1	${\displaystyle{\displaystyle{E^{\prime}}\left(1\right)=\tfrac{1}{2}\pi}}$ `\ccompellintEk@{1} = \tfrac{1}{2}\pi`		EllipticCE(1) = (1)/(2)*Pi	EllipticE[1-(1)^2] == Divide[1,2]*Pi	Successful	Successful	-	Successful [Tested: 1]
19.6#Ex2	${\displaystyle{\displaystyle K\left(1\right)={K^{\prime}}\left(0\right)}}$ `\compellintKk@{1} = \ccompellintKk@{0}`		EllipticK(1) = EllipticCK(0)	EllipticK[(1)^2] == EllipticK[1-(0)^2]	Error	Failure	-	Failed [1 / 1] Result: Indeterminate Test Values: {}
19.6#Ex2	${\displaystyle{\displaystyle{K^{\prime}}\left(0\right)=\infty}}$ `\ccompellintKk@{0} = \infty`		EllipticCK(0) = infinity	EllipticK[1-(0)^2] == Infinity	Error	Failure	-	Failed [1 / 1] Result: Indeterminate Test Values: {}
19.6#Ex3	${\displaystyle{\displaystyle E\left(1\right)={E^{\prime}}\left(0\right)}}$ `\compellintEk@{1} = \ccompellintEk@{0}`		EllipticE(1) = EllipticCE(0)	EllipticE[(1)^2] == EllipticE[1-(0)^2]	Successful	Successful	-	Successful [Tested: 1]
19.6#Ex3	${\displaystyle{\displaystyle{E^{\prime}}\left(0\right)=1}}$ `\ccompellintEk@{0} = 1`		EllipticCE(0) = 1	EllipticE[1-(0)^2] == 1	Successful	Successful	-	Successful [Tested: 1]
19.6#Ex4	${\displaystyle{\displaystyle\Pi\left(k^{2},k\right)=E\left(k\right)/{k^{\prime% }}^{2}}}$ `\compellintPik@{k^{2}}{k} = \compellintEk@{k}/{k^{\prime}}^{2}`	${\displaystyle{\displaystyle k^{2}<1}}$	EllipticPi((k)^(2), k) = EllipticE(k)/(1 - (k)^(2))	EllipticPi[(k)^(2), (k)^2] == EllipticE[(k)^2]/(1 - (k)^(2))	Successful	Successful	-	Successful [Tested: 0]
19.6#Ex5	${\displaystyle{\displaystyle\Pi\left(-k,k\right)=\tfrac{1}{4}\pi(1+k)^{-1}+% \tfrac{1}{2}K\left(k\right)}}$ `\compellintPik@{-k}{k} = \tfrac{1}{4}\pi(1+k)^{-1}+\tfrac{1}{2}\compellintKk@{k}`	${\displaystyle{\displaystyle 0\leq k^{2},k^{2}<1}}$	EllipticPi(- k, k) = (1)/(4)Pi(1 + k)^(- 1)+(1)/(2)*EllipticK(k)	EllipticPi[- k, (k)^2] == Divide[1,4]Pi(1 + k)^(- 1)+Divide[1,2]*EllipticK[(k)^2]	Failure	Failure	Error	Skip - No test values generated
19.6.E3	${\displaystyle{\displaystyle\Pi\left(\alpha^{2},0\right)=\pi/(2\sqrt{1-\alpha^% {2}}),\quad\Pi\left(0,k\right)}}$ `\compellintPik@{\alpha^{2}}{0} = \pi/(2\sqrt{1-\alpha^{2}}),\quad\compellintPik@{0}{k}`	${\displaystyle{\displaystyle-\infty<\alpha^{2},\alpha^{2}<1}}$	EllipticPi((alpha)^(2), 0) = Pi/(2*sqrt(1 - (alpha)^(2)))	EllipticPi[\[Alpha]^(2), (0)^2] == Pi/(2*Sqrt[1 - \[Alpha]^(2)])	Successful	Failure	Skip - symbolical successful subtest	Error
19.6.E3	${\displaystyle{\displaystyle\pi/(2\sqrt{1-\alpha^{2}}),\quad\Pi\left(0,k\right% )=K\left(k\right)}}$ `\pi/(2\sqrt{1-\alpha^{2}}),\quad\compellintPik@{0}{k} = \compellintKk@{k}`	${\displaystyle{\displaystyle-\infty<\alpha^{2},\alpha^{2}<1}}$	Pi/(2*sqrt(1 - (alpha)^(2)))	Pi/(2*Sqrt[1 - \[Alpha]^(2)])	Failure	Failure	Error	Error
19.6.E5	${\displaystyle{\displaystyle\Pi\left(\alpha^{2},k\right)=K\left(k\right)-\Pi% \left(k^{2}/\alpha^{2},k\right)}}$ `\compellintPik@{\alpha^{2}}{k} = \compellintKk@{k}-\compellintPik@{k^{2}/\alpha^{2}}{k}`		EllipticPi((alpha)^(2), k) = EllipticK(k)- EllipticPi((k)^(2)/(alpha)^(2), k)	EllipticPi[\[Alpha]^(2), (k)^2] == EllipticK[(k)^2]- EllipticPi[(k)^(2)/\[Alpha]^(2), (k)^2]	Failure	Failure	Error	Failed [9 / 9] Result: Indeterminate Test Values: {Rule[k, 1], Rule[α, 1.5]} Result: Complex[-1.593078238683172, 2.4424906541753444*^-15] Test Values: {Rule[k, 2], Rule[α, 1.5]} ... skip entries to safe data
19.6#Ex8	${\displaystyle{\displaystyle\Pi\left(\alpha^{2},0\right)=0}}$ `\compellintPik@{\alpha^{2}}{0} = 0`		EllipticPi((alpha)^(2), 0) = 0	EllipticPi[\[Alpha]^(2), (0)^2] == 0	Failure	Failure	Failed [3 / 3] Result: -1.404962946*I Test Values: {alpha = 3/2} Result: 1.813799364 Test Values: {alpha = 1/2} ... skip entries to safe data	Failed [3 / 3] Result: Complex[0.0, -1.4049629462081452] Test Values: {Rule[α, 1.5]} Result: 1.813799364234218 Test Values: {Rule[α, 0.5]} ... skip entries to safe data
19.6#Ex11	${\displaystyle{\displaystyle F\left(0,k\right)=0}}$ `\incellintFk@{0}{k} = 0`		EllipticF(sin(0), k) = 0	EllipticF[0, (k)^2] == 0	Successful	Successful	-	Successful [Tested: 3]
19.6#Ex12	${\displaystyle{\displaystyle F\left(\phi,0\right)=\phi}}$ `\incellintFk@{\phi}{0} = \phi`		EllipticF(sin(phi), 0) = phi	EllipticF[\[Phi], (0)^2] == \[Phi]	Failure	Successful	Failed [2 / 10] Result: .858407346 Test Values: {phi = -2} Result: -.858407346 Test Values: {phi = 2}	Successful [Tested: 10]
19.6#Ex13	${\displaystyle{\displaystyle F\left(\tfrac{1}{2}\pi,1\right)=\infty}}$ `\incellintFk@{\tfrac{1}{2}\pi}{1} = \infty`		EllipticF(sin((1)/(2)*Pi), 1) = infinity	EllipticF[Divide[1,2]*Pi, (1)^2] == Infinity	Error	Failure	-	Failed [1 / 1] Result: Indeterminate Test Values: {}
19.6#Ex14	${\displaystyle{\displaystyle F\left(\tfrac{1}{2}\pi,k\right)=K\left(k\right)}}$ `\incellintFk@{\tfrac{1}{2}\pi}{k} = \compellintKk@{k}`		EllipticF(sin((1)/(2)*Pi), k) = EllipticK(k)	EllipticF[Divide[1,2]*Pi, (k)^2] == EllipticK[(k)^2]	Successful	Successful	-	Successful [Tested: 3]
19.6#Ex15	${\displaystyle{\displaystyle\lim_{\phi\to 0}\ifrac{F\left(\phi,k\right)}{\phi}% =1}}$ `\lim_{\phi\to 0}\ifrac{\incellintFk@{\phi}{k}}{\phi} = 1`		limit((EllipticF(sin(phi), k))/(phi), phi = 0) = 1	Limit[Divide[EllipticF[\[Phi], (k)^2],\[Phi]], \[Phi] -> 0, GenerateConditions->None] == 1	Successful	Successful	-	Successful [Tested: 3]
19.6.E8	${\displaystyle{\displaystyle F\left(\phi,1\right)=(\sin\phi)R_{C}\left(1,{\cos% ^{2}}\phi\right)}}$ `\incellintFk@{\phi}{1} = (\sin@@{\phi})\CarlsonellintRC@{1}{\cos^{2}@@{\phi}}`		Error	EllipticF[\[Phi], (1)^2] == (Sin[\[Phi]])1/Sqrt[(Cos[\[Phi]])^(2)]Hypergeometric2F1[1/2,1/2,3/2,1-(1)/((Cos[\[Phi]])^(2))]	Missing Macro Error	Failure	-	Failed [2 / 10] Result: DirectedInfinity[] Test Values: {Rule[ϕ, -2]} Result: DirectedInfinity[] Test Values: {Rule[ϕ, 2]}
19.6.E8	${\displaystyle{\displaystyle(\sin\phi)R_{C}\left(1,{\cos^{2}}\phi\right)={% \operatorname{gd}^{-1}}\left(\phi\right)}}$ `(\sin@@{\phi})\CarlsonellintRC@{1}{\cos^{2}@@{\phi}} = \aGudermannian@{\phi}`	${\displaystyle{\displaystyle-\frac{1}{2}\pi<(\phi),(\phi)<\frac{1}{2}\pi}}$	Error	(Sin[\[Phi]])1/Sqrt[(Cos[\[Phi]])^(2)]Hypergeometric2F1[1/2,1/2,3/2,1-(1)/((Cos[\[Phi]])^(2))] == InverseGudermannian[\[Phi]]	Missing Macro Error	Failure	-	Successful [Tested: 4]
19.6#Ex16	${\displaystyle{\displaystyle E\left(0,k\right)=0}}$ `\incellintEk@{0}{k} = 0`		EllipticE(sin(0), k) = 0	EllipticE[0, (k)^2] == 0	Successful	Successful	-	Successful [Tested: 3]
19.6#Ex17	${\displaystyle{\displaystyle E\left(\phi,0\right)=\phi}}$ `\incellintEk@{\phi}{0} = \phi`		EllipticE(sin(phi), 0) = phi	EllipticE[\[Phi], (0)^2] == \[Phi]	Failure	Successful	Failed [2 / 10] Result: .858407346 Test Values: {phi = -2} Result: -.858407346 Test Values: {phi = 2}	Successful [Tested: 10]
19.6#Ex18	${\displaystyle{\displaystyle E\left(\tfrac{1}{2}\pi,1\right)=1}}$ `\incellintEk@{\tfrac{1}{2}\pi}{1} = 1`		EllipticE(sin((1)/(2)*Pi), 1) = 1	EllipticE[Divide[1,2]*Pi, (1)^2] == 1	Successful	Successful	-	Successful [Tested: 1]
19.6#Ex19	${\displaystyle{\displaystyle E\left(\phi,1\right)=\sin\phi}}$ `\incellintEk@{\phi}{1} = \sin@@{\phi}`		EllipticE(sin(phi), 1) = sin(phi)	EllipticE[\[Phi], (1)^2] == Sin[\[Phi]]	Successful	Failure	-	Failed [2 / 10] Result: -0.1814051463486368 Test Values: {Rule[ϕ, -2]} Result: 0.1814051463486368 Test Values: {Rule[ϕ, 2]}
19.6#Ex20	${\displaystyle{\displaystyle E\left(\tfrac{1}{2}\pi,k\right)=E\left(k\right)}}$ `\incellintEk@{\tfrac{1}{2}\pi}{k} = \compellintEk@{k}`		EllipticE(sin((1)/(2)*Pi), k) = EllipticE(k)	EllipticE[Divide[1,2]*Pi, (k)^2] == EllipticE[(k)^2]	Successful	Successful	-	Successful [Tested: 3]
19.6.E10	${\displaystyle{\displaystyle\lim_{\phi\to 0}\ifrac{E\left(\phi,k\right)}{\phi}% =1}}$ `\lim_{\phi\to 0}\ifrac{\incellintEk@{\phi}{k}}{\phi} = 1`		limit((EllipticE(sin(phi), k))/(phi), phi = 0) = 1	Limit[Divide[EllipticE[\[Phi], (k)^2],\[Phi]], \[Phi] -> 0, GenerateConditions->None] == 1	Successful	Successful	-	Successful [Tested: 3]
19.6#Ex21	${\displaystyle{\displaystyle\Pi\left(0,\alpha^{2},k\right)=0}}$ `\incellintPik@{0}{\alpha^{2}}{k} = 0`		EllipticPi(sin(0), (alpha)^(2), k) = 0	EllipticPi[\[Alpha]^(2), 0,(k)^2] == 0	Successful	Successful	-	Successful [Tested: 9]
19.6#Ex22	${\displaystyle{\displaystyle\Pi\left(\phi,0,0\right)=\phi}}$ `\incellintPik@{\phi}{0}{0} = \phi`		EllipticPi(sin(phi), 0, 0) = phi	EllipticPi[0, \[Phi],(0)^2] == \[Phi]	Failure	Successful	Failed [2 / 10] Result: .858407346 Test Values: {phi = -2} Result: -.858407346 Test Values: {phi = 2}	Successful [Tested: 10]
19.6#Ex23	${\displaystyle{\displaystyle\Pi\left(\phi,1,0\right)=\tan\phi}}$ `\incellintPik@{\phi}{1}{0} = \tan@@{\phi}`		EllipticPi(sin(phi), 1, 0) = tan(phi)	EllipticPi[1, \[Phi],(0)^2] == Tan[\[Phi]]	Failure	Successful	Failed [2 / 10] Result: -4.370079726 Test Values: {phi = -2} Result: 4.370079726 Test Values: {phi = 2}	Successful [Tested: 10]
19.6#Ex24	${\displaystyle{\displaystyle\Pi\left(\phi,\alpha^{2},0\right)=R_{C}\left(c-1,c% -\alpha^{2}\right)}}$ `\incellintPik@{\phi}{\alpha^{2}}{0} = \CarlsonellintRC@{c-1}{c-\alpha^{2}}`		Error	EllipticPi[\[Alpha]^(2), \[Phi],(0)^2] == 1/Sqrt[c - \[Alpha]^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-(c - 1)/(c - \[Alpha]^(2))]	Missing Macro Error	Failure	-	Failed [180 / 180] Result: Complex[0.4032669574270382, 0.8997227991212673] Test Values: {Rule[c, -1.5], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-0.17167863497284278, 0.9673069947694621] Test Values: {Rule[c, -1.5], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.6#Ex25	${\displaystyle{\displaystyle\Pi\left(\phi,\alpha^{2},1\right)=\frac{1}{1-% \alpha^{2}}\left(R_{C}\left(c,c-1\right)-\alpha^{2}R_{C}\left(c,c-\alpha^{2}% \right)\right)}}$ `\incellintPik@{\phi}{\alpha^{2}}{1} = \frac{1}{1-\alpha^{2}}\left(\CarlsonellintRC@{c}{c-1}-\alpha^{2}\CarlsonellintRC@{c}{c-\alpha^{2}}\right)`		Error	EllipticPi[\[Alpha]^(2), \[Phi],(1)^2] == Divide[1,1 - \[Alpha]^(2)](1/Sqrt[c - 1]Hypergeometric2F1[1/2,1/2,3/2,1-(c)/(c - 1)]- \[Alpha]^(2)* 1/Sqrt[c - \[Alpha]^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-(c)/(c - \[Alpha]^(2))])	Missing Macro Error	Failure	-	Failed [180 / 180] Result: Complex[0.39392267303966433, 0.8870442763896845] Test Values: {Rule[c, -1.5], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-0.15564928813724596, 0.9274825692848638] Test Values: {Rule[c, -1.5], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.6#Ex26	${\displaystyle{\displaystyle\Pi\left(\phi,1,1\right)=\tfrac{1}{2}(R_{C}\left(c% ,c-1\right)+\sqrt{c}(c-1)^{-1})}}$ `\incellintPik@{\phi}{1}{1} = \tfrac{1}{2}(\CarlsonellintRC@{c}{c-1}+\sqrt{c}(c-1)^{-1})`		Error	EllipticPi[1, \[Phi],(1)^2] == Divide[1,2](1/Sqrt[c - 1]Hypergeometric2F1[1/2,1/2,3/2,1-(c)/(c - 1)]+Sqrt[c]*(c - 1)^(- 1))	Missing Macro Error	Failure	-	Failed [60 / 60] Result: Complex[0.42461599644771203, 0.9033982135739806] Test Values: {Rule[c, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-0.19222674503116347, 1.0138365568937844] Test Values: {Rule[c, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.6#Ex27	${\displaystyle{\displaystyle\Pi\left(\phi,0,k\right)=F\left(\phi,k\right)}}$ `\incellintPik@{\phi}{0}{k} = \incellintFk@{\phi}{k}`		EllipticPi(sin(phi), 0, k) = EllipticF(sin(phi), k)	EllipticPi[0, \[Phi],(k)^2] == EllipticF[\[Phi], (k)^2]	Successful	Successful	-	Successful [Tested: 30]
19.6#Ex28	${\displaystyle{\displaystyle\Pi\left(\phi,k^{2},k\right)=\frac{1}{{k^{\prime}}% ^{2}}\left(E\left(\phi,k\right)-\frac{k^{2}}{\Delta}\sin\phi\cos\phi\right)}}$ `\incellintPik@{\phi}{k^{2}}{k} = \frac{1}{{k^{\prime}}^{2}}\left(\incellintEk@{\phi}{k}-\frac{k^{2}}{\Delta}\sin@@{\phi}\cos@@{\phi}\right)`		EllipticPi(sin(phi), (k)^(2), k) = (1)/(1 - (k)^(2))(EllipticE(sin(phi), k)-((k)^(2))/(Delta)sin(phi)*cos(phi))	EllipticPi[(k)^(2), \[Phi],(k)^2] == Divide[1,1 - (k)^(2)](EllipticE[\[Phi], (k)^2]-Divide[(k)^(2),\[CapitalDelta]]Sin[\[Phi]]*Cos[\[Phi]])	Failure	Failure	Failed [300 / 300] Result: Float(infinity)+Float(infinity)I Test Values: {Delta = 1/23^(1/2)+1/2I, phi = 1/23^(1/2)+1/2I, k = 1} Result: -.4574406724+1.116997071I Test Values: {Delta = 1/23^(1/2)+1/2I, phi = 1/23^(1/2)+1/2I, k = 2} ... skip entries to safe data	Failed [300 / 300] Result: Indeterminate Test Values: {Rule[k, 1], Rule[Δ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-0.8161437733664769, 0.6845645198965172] Test Values: {Rule[k, 2], Rule[Δ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} ... skip entries to safe data
19.6#Ex29	${\displaystyle{\displaystyle\Pi\left(\phi,1,k\right)=F\left(\phi,k\right)-% \frac{1}{{k^{\prime}}^{2}}(E\left(\phi,k\right)-\Delta\tan\phi)}}$ `\incellintPik@{\phi}{1}{k} = \incellintFk@{\phi}{k}-\frac{1}{{k^{\prime}}^{2}}(\incellintEk@{\phi}{k}-\Delta\tan@@{\phi})`		EllipticPi(sin(phi), 1, k) = EllipticF(sin(phi), k)-(1)/(1 - (k)^(2))(EllipticE(sin(phi), k)- Deltatan(phi))	EllipticPi[1, \[Phi],(k)^2] == EllipticF[\[Phi], (k)^2]-Divide[1,1 - (k)^(2)](EllipticE[\[Phi], (k)^2]- \[CapitalDelta]Tan[\[Phi]])	Failure	Failure	Failed [300 / 300] Result: Float(infinity)+Float(infinity)I Test Values: {Delta = 1/23^(1/2)+1/2I, phi = 1/23^(1/2)+1/2I, k = 1} Result: -.5381374542+.4861981155I Test Values: {Delta = 1/23^(1/2)+1/2I, phi = 1/23^(1/2)+1/2I, k = 2} ... skip entries to safe data	Failed [300 / 300] Result: Indeterminate Test Values: {Rule[k, 1], Rule[Δ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-0.12805668293605252, 0.0652384492706456] Test Values: {Rule[k, 2], Rule[Δ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} ... skip entries to safe data
19.6#Ex30	${\displaystyle{\displaystyle\Pi\left(\tfrac{1}{2}\pi,\alpha^{2},k\right)=\Pi% \left(\alpha^{2},k\right)}}$ `\incellintPik@{\tfrac{1}{2}\pi}{\alpha^{2}}{k} = \compellintPik@{\alpha^{2}}{k}`		EllipticPi(sin((1)/(2)*Pi), (alpha)^(2), k) = EllipticPi((alpha)^(2), k)	EllipticPi[\[Alpha]^(2), Divide[1,2]*Pi,(k)^2] == EllipticPi[\[Alpha]^(2), (k)^2]	Successful	Successful	-	Successful [Tested: 9]
19.6#Ex31	${\displaystyle{\displaystyle\lim_{\phi\to 0}\ifrac{\Pi\left(\phi,\alpha^{2},k% \right)}{\phi}=1}}$ `\lim_{\phi\to 0}\ifrac{\incellintPik@{\phi}{\alpha^{2}}{k}}{\phi} = 1`		limit((EllipticPi(sin(phi), (alpha)^(2), k))/(phi), phi = 0) = 1	Limit[Divide[EllipticPi[\[Alpha]^(2), \[Phi],(k)^2],\[Phi]], \[Phi] -> 0, GenerateConditions->None] == 1	Successful	Successful	-	Successful [Tested: 9]
19.6#Ex32	${\displaystyle{\displaystyle R_{C}\left(x,x\right)=x^{-1/2}}}$ `\CarlsonellintRC@{x}{x} = x^{-1/2}`		Error	1/Sqrt[x]*Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(x)] == (x)^(- 1/2)	Missing Macro Error	Successful	-	Successful [Tested: 3]
19.6#Ex33	${\displaystyle{\displaystyle R_{C}\left(\lambda x,\lambda y\right)=\lambda^{-1% /2}R_{C}\left(x,y\right)}}$ `\CarlsonellintRC@{\lambda x}{\lambda y} = \lambda^{-1/2}\CarlsonellintRC@{x}{y}`		Error	1/Sqrt[\[Lambda]y]Hypergeometric2F1[1/2,1/2,3/2,1-(\[Lambda]x)/(\[Lambda]y)] == \[Lambda]^(- 1/2)* 1/Sqrt[y]*Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(y)]	Missing Macro Error	Failure	-	Failed [75 / 180] Result: Complex[2.0541315094196904, 2.1051836996148214] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[2.941079989400646, 0.036099349881403064] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.6#Ex35	${\displaystyle{\displaystyle R_{C}\left(0,y\right)=\tfrac{1}{2}\pi y^{-1/2}}}$ `\CarlsonellintRC@{0}{y} = \tfrac{1}{2}\pi y^{-1/2}`	${\displaystyle{\displaystyle\|\operatorname{ph}y\|<\pi}}$	Error	1/Sqrt[y]Hypergeometric2F1[1/2,1/2,3/2,1-(0)/(y)] == Divide[1,2]Pi*(y)^(- 1/2)	Missing Macro Error	Successful	-	Successful [Tested: 3]
19.6#Ex36	${\displaystyle{\displaystyle R_{C}\left(0,y\right)=0}}$ `\CarlsonellintRC@{0}{y} = 0`	${\displaystyle{\displaystyle y<0}}$	Error	1/Sqrt[y]*Hypergeometric2F1[1/2,1/2,3/2,1-(0)/(y)] == 0	Missing Macro Error	Failure	-	Failed [3 / 3] Result: Complex[0.0, -1.2825498301618643] Test Values: {Rule[y, -1.5]} Result: Complex[0.0, -2.221441469079183] Test Values: {Rule[y, -0.5]} ... skip entries to safe data

@@ Line 14: / Line 14: @@
 ! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
 |-
-| [https://dlmf.nist.gov/19.6#Ex1 19.6#Ex1] || [[Item:Q6141|<math>\compellintKk@{0} = \compellintEk@{0}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\compellintKk@{0} = \compellintEk@{0}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticK(0) = EllipticE(0)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticK[(0)^2] == EllipticE[(0)^2]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
+| [https://dlmf.nist.gov/19.6#Ex1 19.6#Ex1] || <math qid="Q6141">\compellintKk@{0} = \compellintEk@{0}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\compellintKk@{0} = \compellintEk@{0}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticK(0) = EllipticE(0)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticK[(0)^2] == EllipticE[(0)^2]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
 |-
-| [https://dlmf.nist.gov/19.6#Ex1 19.6#Ex1] || [[Item:Q6141|<math>\compellintEk@{0} = \ccompellintKk@{1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\compellintEk@{0} = \ccompellintKk@{1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticE(0) = EllipticCK(1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticE[(0)^2] == EllipticK[1-(1)^2]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
+| [https://dlmf.nist.gov/19.6#Ex1 19.6#Ex1] || <math qid="Q6141">\compellintEk@{0} = \ccompellintKk@{1}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\compellintEk@{0} = \ccompellintKk@{1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticE(0) = EllipticCK(1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticE[(0)^2] == EllipticK[1-(1)^2]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
 |-
-| [https://dlmf.nist.gov/19.6#Ex1 19.6#Ex1] || [[Item:Q6141|<math>\ccompellintKk@{1} = \ccompellintEk@{1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ccompellintKk@{1} = \ccompellintEk@{1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticCK(1) = EllipticCE(1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticK[1-(1)^2] == EllipticE[1-(1)^2]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
+| [https://dlmf.nist.gov/19.6#Ex1 19.6#Ex1] || <math qid="Q6141">\ccompellintKk@{1} = \ccompellintEk@{1}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ccompellintKk@{1} = \ccompellintEk@{1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticCK(1) = EllipticCE(1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticK[1-(1)^2] == EllipticE[1-(1)^2]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
 |-
-| [https://dlmf.nist.gov/19.6#Ex1 19.6#Ex1] || [[Item:Q6141|<math>\ccompellintEk@{1} = \tfrac{1}{2}\pi</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ccompellintEk@{1} = \tfrac{1}{2}\pi</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticCE(1) = (1)/(2)*Pi</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticE[1-(1)^2] == Divide[1,2]*Pi</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
+| [https://dlmf.nist.gov/19.6#Ex1 19.6#Ex1] || <math qid="Q6141">\ccompellintEk@{1} = \tfrac{1}{2}\pi</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ccompellintEk@{1} = \tfrac{1}{2}\pi</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticCE(1) = (1)/(2)*Pi</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticE[1-(1)^2] == Divide[1,2]*Pi</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
 |-
-| [https://dlmf.nist.gov/19.6#Ex2 19.6#Ex2] || [[Item:Q6142|<math>\compellintKk@{1} = \ccompellintKk@{0}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\compellintKk@{1} = \ccompellintKk@{0}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticK(1) = EllipticCK(0)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticK[(1)^2] == EllipticK[1-(0)^2]</syntaxhighlight> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 1]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
+| [https://dlmf.nist.gov/19.6#Ex2 19.6#Ex2] || <math qid="Q6142">\compellintKk@{1} = \ccompellintKk@{0}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\compellintKk@{1} = \ccompellintKk@{0}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticK(1) = EllipticCK(0)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticK[(1)^2] == EllipticK[1-(0)^2]</syntaxhighlight> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 1]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
 Test Values: {}</syntaxhighlight><br></div></div>
 |-
-| [https://dlmf.nist.gov/19.6#Ex2 19.6#Ex2] || [[Item:Q6142|<math>\ccompellintKk@{0} = \infty</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ccompellintKk@{0} = \infty</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticCK(0) = infinity</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticK[1-(0)^2] == Infinity</syntaxhighlight> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 1]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
+| [https://dlmf.nist.gov/19.6#Ex2 19.6#Ex2] || <math qid="Q6142">\ccompellintKk@{0} = \infty</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ccompellintKk@{0} = \infty</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticCK(0) = infinity</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticK[1-(0)^2] == Infinity</syntaxhighlight> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 1]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
 Test Values: {}</syntaxhighlight><br></div></div>
 |-
-| [https://dlmf.nist.gov/19.6#Ex3 19.6#Ex3] || [[Item:Q6143|<math>\compellintEk@{1} = \ccompellintEk@{0}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\compellintEk@{1} = \ccompellintEk@{0}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticE(1) = EllipticCE(0)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticE[(1)^2] == EllipticE[1-(0)^2]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
+| [https://dlmf.nist.gov/19.6#Ex3 19.6#Ex3] || <math qid="Q6143">\compellintEk@{1} = \ccompellintEk@{0}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\compellintEk@{1} = \ccompellintEk@{0}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticE(1) = EllipticCE(0)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticE[(1)^2] == EllipticE[1-(0)^2]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
 |-
-| [https://dlmf.nist.gov/19.6#Ex3 19.6#Ex3] || [[Item:Q6143|<math>\ccompellintEk@{0} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ccompellintEk@{0} = 1</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticCE(0) = 1</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticE[1-(0)^2] == 1</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
+| [https://dlmf.nist.gov/19.6#Ex3 19.6#Ex3] || <math qid="Q6143">\ccompellintEk@{0} = 1</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ccompellintEk@{0} = 1</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticCE(0) = 1</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticE[1-(0)^2] == 1</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
 |-
-| [https://dlmf.nist.gov/19.6#Ex4 19.6#Ex4] || [[Item:Q6144|<math>\compellintPik@{k^{2}}{k} = \compellintEk@{k}/{k^{\prime}}^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\compellintPik@{k^{2}}{k} = \compellintEk@{k}/{k^{\prime}}^{2}</syntaxhighlight> || <math>k^{2} < 1</math> || <syntaxhighlight lang=mathematica>EllipticPi((k)^(2), k) = EllipticE(k)/(1 - (k)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticPi[(k)^(2), (k)^2] == EllipticE[(k)^2]/(1 - (k)^(2))</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 0]
+| [https://dlmf.nist.gov/19.6#Ex4 19.6#Ex4] || <math qid="Q6144">\compellintPik@{k^{2}}{k} = \compellintEk@{k}/{k^{\prime}}^{2}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\compellintPik@{k^{2}}{k} = \compellintEk@{k}/{k^{\prime}}^{2}</syntaxhighlight> || <math>k^{2} < 1</math> || <syntaxhighlight lang=mathematica>EllipticPi((k)^(2), k) = EllipticE(k)/(1 - (k)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticPi[(k)^(2), (k)^2] == EllipticE[(k)^2]/(1 - (k)^(2))</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 0]
 |-
-| [https://dlmf.nist.gov/19.6#Ex5 19.6#Ex5] || [[Item:Q6145|<math>\compellintPik@{-k}{k} = \tfrac{1}{4}\pi(1+k)^{-1}+\tfrac{1}{2}\compellintKk@{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\compellintPik@{-k}{k} = \tfrac{1}{4}\pi(1+k)^{-1}+\tfrac{1}{2}\compellintKk@{k}</syntaxhighlight> || <math>0 \leq k^{2}, k^{2} < 1</math> || <syntaxhighlight lang=mathematica>EllipticPi(- k, k) = (1)/(4)*Pi*(1 + k)^(- 1)+(1)/(2)*EllipticK(k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticPi[- k, (k)^2] == Divide[1,4]*Pi*(1 + k)^(- 1)+Divide[1,2]*EllipticK[(k)^2]</syntaxhighlight> || Failure || Failure || Error || Skip - No test values generated
+| [https://dlmf.nist.gov/19.6#Ex5 19.6#Ex5] || <math qid="Q6145">\compellintPik@{-k}{k} = \tfrac{1}{4}\pi(1+k)^{-1}+\tfrac{1}{2}\compellintKk@{k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\compellintPik@{-k}{k} = \tfrac{1}{4}\pi(1+k)^{-1}+\tfrac{1}{2}\compellintKk@{k}</syntaxhighlight> || <math>0 \leq k^{2}, k^{2} < 1</math> || <syntaxhighlight lang=mathematica>EllipticPi(- k, k) = (1)/(4)*Pi*(1 + k)^(- 1)+(1)/(2)*EllipticK(k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticPi[- k, (k)^2] == Divide[1,4]*Pi*(1 + k)^(- 1)+Divide[1,2]*EllipticK[(k)^2]</syntaxhighlight> || Failure || Failure || Error || Skip - No test values generated
 |-
-| [https://dlmf.nist.gov/19.6.E3 19.6.E3] || [[Item:Q6146|<math>\compellintPik@{\alpha^{2}}{0} = \pi/(2\sqrt{1-\alpha^{2}}),\quad\compellintPik@{0}{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\compellintPik@{\alpha^{2}}{0} = \pi/(2\sqrt{1-\alpha^{2}}),\quad\compellintPik@{0}{k}</syntaxhighlight> || <math>-\infty < \alpha^{2}, \alpha^{2} < 1</math> || <syntaxhighlight lang=mathematica>EllipticPi((alpha)^(2), 0) = Pi/(2*sqrt(1 - (alpha)^(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticPi[\[Alpha]^(2), (0)^2] == Pi/(2*Sqrt[1 - \[Alpha]^(2)])</syntaxhighlight> || Successful || Failure || Skip - symbolical successful subtest || Error
+| [https://dlmf.nist.gov/19.6.E3 19.6.E3] || <math qid="Q6146">\compellintPik@{\alpha^{2}}{0} = \pi/(2\sqrt{1-\alpha^{2}}),\quad\compellintPik@{0}{k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\compellintPik@{\alpha^{2}}{0} = \pi/(2\sqrt{1-\alpha^{2}}),\quad\compellintPik@{0}{k}</syntaxhighlight> || <math>-\infty < \alpha^{2}, \alpha^{2} < 1</math> || <syntaxhighlight lang=mathematica>EllipticPi((alpha)^(2), 0) = Pi/(2*sqrt(1 - (alpha)^(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticPi[\[Alpha]^(2), (0)^2] == Pi/(2*Sqrt[1 - \[Alpha]^(2)])</syntaxhighlight> || Successful || Failure || Skip - symbolical successful subtest || Error
 |-
-| [https://dlmf.nist.gov/19.6.E3 19.6.E3] || [[Item:Q6146|<math>\pi/(2\sqrt{1-\alpha^{2}}),\quad\compellintPik@{0}{k} = \compellintKk@{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\pi/(2\sqrt{1-\alpha^{2}}),\quad\compellintPik@{0}{k} = \compellintKk@{k}</syntaxhighlight> || <math>-\infty < \alpha^{2}, \alpha^{2} < 1</math> || <syntaxhighlight lang=mathematica>Pi/(2*sqrt(1 - (alpha)^(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Pi/(2*Sqrt[1 - \[Alpha]^(2)])</syntaxhighlight> || Failure || Failure || Error || Error
+| [https://dlmf.nist.gov/19.6.E3 19.6.E3] || <math qid="Q6146">\pi/(2\sqrt{1-\alpha^{2}}),\quad\compellintPik@{0}{k} = \compellintKk@{k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\pi/(2\sqrt{1-\alpha^{2}}),\quad\compellintPik@{0}{k} = \compellintKk@{k}</syntaxhighlight> || <math>-\infty < \alpha^{2}, \alpha^{2} < 1</math> || <syntaxhighlight lang=mathematica>Pi/(2*sqrt(1 - (alpha)^(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Pi/(2*Sqrt[1 - \[Alpha]^(2)])</syntaxhighlight> || Failure || Failure || Error || Error
 |-
-| [https://dlmf.nist.gov/19.6.E5 19.6.E5] || [[Item:Q6149|<math>\compellintPik@{\alpha^{2}}{k} = \compellintKk@{k}-\compellintPik@{k^{2}/\alpha^{2}}{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\compellintPik@{\alpha^{2}}{k} = \compellintKk@{k}-\compellintPik@{k^{2}/\alpha^{2}}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticPi((alpha)^(2), k) = EllipticK(k)- EllipticPi((k)^(2)/(alpha)^(2), k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticPi[\[Alpha]^(2), (k)^2] == EllipticK[(k)^2]- EllipticPi[(k)^(2)/\[Alpha]^(2), (k)^2]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
+| [https://dlmf.nist.gov/19.6.E5 19.6.E5] || <math qid="Q6149">\compellintPik@{\alpha^{2}}{k} = \compellintKk@{k}-\compellintPik@{k^{2}/\alpha^{2}}{k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\compellintPik@{\alpha^{2}}{k} = \compellintKk@{k}-\compellintPik@{k^{2}/\alpha^{2}}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticPi((alpha)^(2), k) = EllipticK(k)- EllipticPi((k)^(2)/(alpha)^(2), k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticPi[\[Alpha]^(2), (k)^2] == EllipticK[(k)^2]- EllipticPi[(k)^(2)/\[Alpha]^(2), (k)^2]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
 Test Values: {Rule[k, 1], Rule[α, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.593078238683172, 2.4424906541753444*^-15]
 Test Values: {Rule[k, 2], Rule[α, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/19.6#Ex8 19.6#Ex8] || [[Item:Q6150|<math>\compellintPik@{\alpha^{2}}{0} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\compellintPik@{\alpha^{2}}{0} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticPi((alpha)^(2), 0) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticPi[\[Alpha]^(2), (0)^2] == 0</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.404962946*I
+| [https://dlmf.nist.gov/19.6#Ex8 19.6#Ex8] || <math qid="Q6150">\compellintPik@{\alpha^{2}}{0} = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\compellintPik@{\alpha^{2}}{0} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticPi((alpha)^(2), 0) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticPi[\[Alpha]^(2), (0)^2] == 0</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.404962946*I
 Test Values: {alpha = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.813799364
 Test Values: {alpha = 1/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.0, -1.4049629462081452]
@@ Line 50: / Line 50: @@
 Test Values: {Rule[α, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/19.6#Ex11 19.6#Ex11] || [[Item:Q6153|<math>\incellintFk@{0}{k} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintFk@{0}{k} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticF(sin(0), k) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticF[0, (k)^2] == 0</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 3]
+| [https://dlmf.nist.gov/19.6#Ex11 19.6#Ex11] || <math qid="Q6153">\incellintFk@{0}{k} = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintFk@{0}{k} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticF(sin(0), k) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticF[0, (k)^2] == 0</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 3]
 |-
-| [https://dlmf.nist.gov/19.6#Ex12 19.6#Ex12] || [[Item:Q6154|<math>\incellintFk@{\phi}{0} = \phi</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintFk@{\phi}{0} = \phi</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticF(sin(phi), 0) = phi</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticF[\[Phi], (0)^2] == \[Phi]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 10]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .858407346
+| [https://dlmf.nist.gov/19.6#Ex12 19.6#Ex12] || <math qid="Q6154">\incellintFk@{\phi}{0} = \phi</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintFk@{\phi}{0} = \phi</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticF(sin(phi), 0) = phi</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticF[\[Phi], (0)^2] == \[Phi]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 10]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .858407346
 Test Values: {phi = -2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.858407346
 Test Values: {phi = 2}</syntaxhighlight><br></div></div> || Successful [Tested: 10]
 |-
-| [https://dlmf.nist.gov/19.6#Ex13 19.6#Ex13] || [[Item:Q6155|<math>\incellintFk@{\tfrac{1}{2}\pi}{1} = \infty</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintFk@{\tfrac{1}{2}\pi}{1} = \infty</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticF(sin((1)/(2)*Pi), 1) = infinity</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticF[Divide[1,2]*Pi, (1)^2] == Infinity</syntaxhighlight> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 1]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
+| [https://dlmf.nist.gov/19.6#Ex13 19.6#Ex13] || <math qid="Q6155">\incellintFk@{\tfrac{1}{2}\pi}{1} = \infty</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintFk@{\tfrac{1}{2}\pi}{1} = \infty</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticF(sin((1)/(2)*Pi), 1) = infinity</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticF[Divide[1,2]*Pi, (1)^2] == Infinity</syntaxhighlight> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 1]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
 Test Values: {}</syntaxhighlight><br></div></div>
 |-
-| [https://dlmf.nist.gov/19.6#Ex14 19.6#Ex14] || [[Item:Q6156|<math>\incellintFk@{\tfrac{1}{2}\pi}{k} = \compellintKk@{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintFk@{\tfrac{1}{2}\pi}{k} = \compellintKk@{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticF(sin((1)/(2)*Pi), k) = EllipticK(k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticF[Divide[1,2]*Pi, (k)^2] == EllipticK[(k)^2]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 3]
+| [https://dlmf.nist.gov/19.6#Ex14 19.6#Ex14] || <math qid="Q6156">\incellintFk@{\tfrac{1}{2}\pi}{k} = \compellintKk@{k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintFk@{\tfrac{1}{2}\pi}{k} = \compellintKk@{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticF(sin((1)/(2)*Pi), k) = EllipticK(k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticF[Divide[1,2]*Pi, (k)^2] == EllipticK[(k)^2]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 3]
 |-
-| [https://dlmf.nist.gov/19.6#Ex15 19.6#Ex15] || [[Item:Q6157|<math>\lim_{\phi\to 0}\ifrac{\incellintFk@{\phi}{k}}{\phi} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\lim_{\phi\to 0}\ifrac{\incellintFk@{\phi}{k}}{\phi} = 1</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>limit((EllipticF(sin(phi), k))/(phi), phi = 0) = 1</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[Divide[EllipticF[\[Phi], (k)^2],\[Phi]], \[Phi] -> 0, GenerateConditions->None] == 1</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 3]
+| [https://dlmf.nist.gov/19.6#Ex15 19.6#Ex15] || <math qid="Q6157">\lim_{\phi\to 0}\ifrac{\incellintFk@{\phi}{k}}{\phi} = 1</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\lim_{\phi\to 0}\ifrac{\incellintFk@{\phi}{k}}{\phi} = 1</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>limit((EllipticF(sin(phi), k))/(phi), phi = 0) = 1</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[Divide[EllipticF[\[Phi], (k)^2],\[Phi]], \[Phi] -> 0, GenerateConditions->None] == 1</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 3]
 |-
-| [https://dlmf.nist.gov/19.6.E8 19.6.E8] || [[Item:Q6158|<math>\incellintFk@{\phi}{1} = (\sin@@{\phi})\CarlsonellintRC@{1}{\cos^{2}@@{\phi}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintFk@{\phi}{1} = (\sin@@{\phi})\CarlsonellintRC@{1}{\cos^{2}@@{\phi}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticF[\[Phi], (1)^2] == (Sin[\[Phi]])*1/Sqrt[(Cos[\[Phi]])^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-(1)/((Cos[\[Phi]])^(2))]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 10]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: DirectedInfinity[]
+| [https://dlmf.nist.gov/19.6.E8 19.6.E8] || <math qid="Q6158">\incellintFk@{\phi}{1} = (\sin@@{\phi})\CarlsonellintRC@{1}{\cos^{2}@@{\phi}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintFk@{\phi}{1} = (\sin@@{\phi})\CarlsonellintRC@{1}{\cos^{2}@@{\phi}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticF[\[Phi], (1)^2] == (Sin[\[Phi]])*1/Sqrt[(Cos[\[Phi]])^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-(1)/((Cos[\[Phi]])^(2))]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 10]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: DirectedInfinity[]
 Test Values: {Rule[ϕ, -2]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: DirectedInfinity[]
 Test Values: {Rule[ϕ, 2]}</syntaxhighlight><br></div></div>
 |-
-| [https://dlmf.nist.gov/19.6.E8 19.6.E8] || [[Item:Q6158|<math>(\sin@@{\phi})\CarlsonellintRC@{1}{\cos^{2}@@{\phi}} = \aGudermannian@{\phi}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(\sin@@{\phi})\CarlsonellintRC@{1}{\cos^{2}@@{\phi}} = \aGudermannian@{\phi}</syntaxhighlight> || <math>-\frac{1}{2}\pi < (\phi), (\phi) < \frac{1}{2}\pi</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Sin[\[Phi]])*1/Sqrt[(Cos[\[Phi]])^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-(1)/((Cos[\[Phi]])^(2))] == InverseGudermannian[\[Phi]]</syntaxhighlight> || Missing Macro Error || Failure || - || Successful [Tested: 4]
+| [https://dlmf.nist.gov/19.6.E8 19.6.E8] || <math qid="Q6158">(\sin@@{\phi})\CarlsonellintRC@{1}{\cos^{2}@@{\phi}} = \aGudermannian@{\phi}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(\sin@@{\phi})\CarlsonellintRC@{1}{\cos^{2}@@{\phi}} = \aGudermannian@{\phi}</syntaxhighlight> || <math>-\frac{1}{2}\pi < (\phi), (\phi) < \frac{1}{2}\pi</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Sin[\[Phi]])*1/Sqrt[(Cos[\[Phi]])^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-(1)/((Cos[\[Phi]])^(2))] == InverseGudermannian[\[Phi]]</syntaxhighlight> || Missing Macro Error || Failure || - || Successful [Tested: 4]
 |-
-| [https://dlmf.nist.gov/19.6#Ex16 19.6#Ex16] || [[Item:Q6159|<math>\incellintEk@{0}{k} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintEk@{0}{k} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticE(sin(0), k) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticE[0, (k)^2] == 0</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 3]
+| [https://dlmf.nist.gov/19.6#Ex16 19.6#Ex16] || <math qid="Q6159">\incellintEk@{0}{k} = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintEk@{0}{k} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticE(sin(0), k) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticE[0, (k)^2] == 0</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 3]
 |-
-| [https://dlmf.nist.gov/19.6#Ex17 19.6#Ex17] || [[Item:Q6160|<math>\incellintEk@{\phi}{0} = \phi</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintEk@{\phi}{0} = \phi</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticE(sin(phi), 0) = phi</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticE[\[Phi], (0)^2] == \[Phi]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 10]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .858407346
+| [https://dlmf.nist.gov/19.6#Ex17 19.6#Ex17] || <math qid="Q6160">\incellintEk@{\phi}{0} = \phi</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintEk@{\phi}{0} = \phi</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticE(sin(phi), 0) = phi</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticE[\[Phi], (0)^2] == \[Phi]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 10]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .858407346
 Test Values: {phi = -2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.858407346
 Test Values: {phi = 2}</syntaxhighlight><br></div></div> || Successful [Tested: 10]
 |-
-| [https://dlmf.nist.gov/19.6#Ex18 19.6#Ex18] || [[Item:Q6161|<math>\incellintEk@{\tfrac{1}{2}\pi}{1} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintEk@{\tfrac{1}{2}\pi}{1} = 1</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticE(sin((1)/(2)*Pi), 1) = 1</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticE[Divide[1,2]*Pi, (1)^2] == 1</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
+| [https://dlmf.nist.gov/19.6#Ex18 19.6#Ex18] || <math qid="Q6161">\incellintEk@{\tfrac{1}{2}\pi}{1} = 1</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintEk@{\tfrac{1}{2}\pi}{1} = 1</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticE(sin((1)/(2)*Pi), 1) = 1</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticE[Divide[1,2]*Pi, (1)^2] == 1</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
 |-
-| [https://dlmf.nist.gov/19.6#Ex19 19.6#Ex19] || [[Item:Q6162|<math>\incellintEk@{\phi}{1} = \sin@@{\phi}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintEk@{\phi}{1} = \sin@@{\phi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticE(sin(phi), 1) = sin(phi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticE[\[Phi], (1)^2] == Sin[\[Phi]]</syntaxhighlight> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 10]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -0.1814051463486368
+| [https://dlmf.nist.gov/19.6#Ex19 19.6#Ex19] || <math qid="Q6162">\incellintEk@{\phi}{1} = \sin@@{\phi}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintEk@{\phi}{1} = \sin@@{\phi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticE(sin(phi), 1) = sin(phi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticE[\[Phi], (1)^2] == Sin[\[Phi]]</syntaxhighlight> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 10]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -0.1814051463486368
 Test Values: {Rule[ϕ, -2]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 0.1814051463486368
 Test Values: {Rule[ϕ, 2]}</syntaxhighlight><br></div></div>
 |-
-| [https://dlmf.nist.gov/19.6#Ex20 19.6#Ex20] || [[Item:Q6163|<math>\incellintEk@{\tfrac{1}{2}\pi}{k} = \compellintEk@{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintEk@{\tfrac{1}{2}\pi}{k} = \compellintEk@{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticE(sin((1)/(2)*Pi), k) = EllipticE(k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticE[Divide[1,2]*Pi, (k)^2] == EllipticE[(k)^2]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 3]
+| [https://dlmf.nist.gov/19.6#Ex20 19.6#Ex20] || <math qid="Q6163">\incellintEk@{\tfrac{1}{2}\pi}{k} = \compellintEk@{k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintEk@{\tfrac{1}{2}\pi}{k} = \compellintEk@{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticE(sin((1)/(2)*Pi), k) = EllipticE(k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticE[Divide[1,2]*Pi, (k)^2] == EllipticE[(k)^2]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 3]
 |-
-| [https://dlmf.nist.gov/19.6.E10 19.6.E10] || [[Item:Q6164|<math>\lim_{\phi\to 0}\ifrac{\incellintEk@{\phi}{k}}{\phi} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\lim_{\phi\to 0}\ifrac{\incellintEk@{\phi}{k}}{\phi} = 1</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>limit((EllipticE(sin(phi), k))/(phi), phi = 0) = 1</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[Divide[EllipticE[\[Phi], (k)^2],\[Phi]], \[Phi] -> 0, GenerateConditions->None] == 1</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 3]
+| [https://dlmf.nist.gov/19.6.E10 19.6.E10] || <math qid="Q6164">\lim_{\phi\to 0}\ifrac{\incellintEk@{\phi}{k}}{\phi} = 1</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\lim_{\phi\to 0}\ifrac{\incellintEk@{\phi}{k}}{\phi} = 1</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>limit((EllipticE(sin(phi), k))/(phi), phi = 0) = 1</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[Divide[EllipticE[\[Phi], (k)^2],\[Phi]], \[Phi] -> 0, GenerateConditions->None] == 1</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 3]
 |-
-| [https://dlmf.nist.gov/19.6#Ex21 19.6#Ex21] || [[Item:Q6165|<math>\incellintPik@{0}{\alpha^{2}}{k} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintPik@{0}{\alpha^{2}}{k} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticPi(sin(0), (alpha)^(2), k) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticPi[\[Alpha]^(2), 0,(k)^2] == 0</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 9]
+| [https://dlmf.nist.gov/19.6#Ex21 19.6#Ex21] || <math qid="Q6165">\incellintPik@{0}{\alpha^{2}}{k} = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintPik@{0}{\alpha^{2}}{k} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticPi(sin(0), (alpha)^(2), k) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticPi[\[Alpha]^(2), 0,(k)^2] == 0</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 9]
 |-
-| [https://dlmf.nist.gov/19.6#Ex22 19.6#Ex22] || [[Item:Q6166|<math>\incellintPik@{\phi}{0}{0} = \phi</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintPik@{\phi}{0}{0} = \phi</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticPi(sin(phi), 0, 0) = phi</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticPi[0, \[Phi],(0)^2] == \[Phi]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 10]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .858407346
+| [https://dlmf.nist.gov/19.6#Ex22 19.6#Ex22] || <math qid="Q6166">\incellintPik@{\phi}{0}{0} = \phi</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintPik@{\phi}{0}{0} = \phi</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticPi(sin(phi), 0, 0) = phi</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticPi[0, \[Phi],(0)^2] == \[Phi]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 10]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .858407346
 Test Values: {phi = -2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.858407346
 Test Values: {phi = 2}</syntaxhighlight><br></div></div> || Successful [Tested: 10]
 |-
-| [https://dlmf.nist.gov/19.6#Ex23 19.6#Ex23] || [[Item:Q6167|<math>\incellintPik@{\phi}{1}{0} = \tan@@{\phi}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintPik@{\phi}{1}{0} = \tan@@{\phi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticPi(sin(phi), 1, 0) = tan(phi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticPi[1, \[Phi],(0)^2] == Tan[\[Phi]]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 10]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -4.370079726
+| [https://dlmf.nist.gov/19.6#Ex23 19.6#Ex23] || <math qid="Q6167">\incellintPik@{\phi}{1}{0} = \tan@@{\phi}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintPik@{\phi}{1}{0} = \tan@@{\phi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticPi(sin(phi), 1, 0) = tan(phi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticPi[1, \[Phi],(0)^2] == Tan[\[Phi]]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 10]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -4.370079726
 Test Values: {phi = -2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 4.370079726
 Test Values: {phi = 2}</syntaxhighlight><br></div></div> || Successful [Tested: 10]
 |-
-| [https://dlmf.nist.gov/19.6#Ex24 19.6#Ex24] || [[Item:Q6168|<math>\incellintPik@{\phi}{\alpha^{2}}{0} = \CarlsonellintRC@{c-1}{c-\alpha^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintPik@{\phi}{\alpha^{2}}{0} = \CarlsonellintRC@{c-1}{c-\alpha^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticPi[\[Alpha]^(2), \[Phi],(0)^2] == 1/Sqrt[c - \[Alpha]^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-(c - 1)/(c - \[Alpha]^(2))]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [180 / 180]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.4032669574270382, 0.8997227991212673]
+| [https://dlmf.nist.gov/19.6#Ex24 19.6#Ex24] || <math qid="Q6168">\incellintPik@{\phi}{\alpha^{2}}{0} = \CarlsonellintRC@{c-1}{c-\alpha^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintPik@{\phi}{\alpha^{2}}{0} = \CarlsonellintRC@{c-1}{c-\alpha^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticPi[\[Alpha]^(2), \[Phi],(0)^2] == 1/Sqrt[c - \[Alpha]^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-(c - 1)/(c - \[Alpha]^(2))]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [180 / 180]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.4032669574270382, 0.8997227991212673]
 Test Values: {Rule[c, -1.5], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.17167863497284278, 0.9673069947694621]
 Test Values: {Rule[c, -1.5], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/19.6#Ex25 19.6#Ex25] || [[Item:Q6169|<math>\incellintPik@{\phi}{\alpha^{2}}{1} = \frac{1}{1-\alpha^{2}}\left(\CarlsonellintRC@{c}{c-1}-\alpha^{2}\CarlsonellintRC@{c}{c-\alpha^{2}}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintPik@{\phi}{\alpha^{2}}{1} = \frac{1}{1-\alpha^{2}}\left(\CarlsonellintRC@{c}{c-1}-\alpha^{2}\CarlsonellintRC@{c}{c-\alpha^{2}}\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticPi[\[Alpha]^(2), \[Phi],(1)^2] == Divide[1,1 - \[Alpha]^(2)]*(1/Sqrt[c - 1]*Hypergeometric2F1[1/2,1/2,3/2,1-(c)/(c - 1)]- \[Alpha]^(2)* 1/Sqrt[c - \[Alpha]^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-(c)/(c - \[Alpha]^(2))])</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [180 / 180]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.39392267303966433, 0.8870442763896845]
+| [https://dlmf.nist.gov/19.6#Ex25 19.6#Ex25] || <math qid="Q6169">\incellintPik@{\phi}{\alpha^{2}}{1} = \frac{1}{1-\alpha^{2}}\left(\CarlsonellintRC@{c}{c-1}-\alpha^{2}\CarlsonellintRC@{c}{c-\alpha^{2}}\right)</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintPik@{\phi}{\alpha^{2}}{1} = \frac{1}{1-\alpha^{2}}\left(\CarlsonellintRC@{c}{c-1}-\alpha^{2}\CarlsonellintRC@{c}{c-\alpha^{2}}\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticPi[\[Alpha]^(2), \[Phi],(1)^2] == Divide[1,1 - \[Alpha]^(2)]*(1/Sqrt[c - 1]*Hypergeometric2F1[1/2,1/2,3/2,1-(c)/(c - 1)]- \[Alpha]^(2)* 1/Sqrt[c - \[Alpha]^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-(c)/(c - \[Alpha]^(2))])</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [180 / 180]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.39392267303966433, 0.8870442763896845]
 Test Values: {Rule[c, -1.5], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.15564928813724596, 0.9274825692848638]
 Test Values: {Rule[c, -1.5], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/19.6#Ex26 19.6#Ex26] || [[Item:Q6170|<math>\incellintPik@{\phi}{1}{1} = \tfrac{1}{2}(\CarlsonellintRC@{c}{c-1}+\sqrt{c}(c-1)^{-1})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintPik@{\phi}{1}{1} = \tfrac{1}{2}(\CarlsonellintRC@{c}{c-1}+\sqrt{c}(c-1)^{-1})</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticPi[1, \[Phi],(1)^2] == Divide[1,2]*(1/Sqrt[c - 1]*Hypergeometric2F1[1/2,1/2,3/2,1-(c)/(c - 1)]+Sqrt[c]*(c - 1)^(- 1))</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [60 / 60]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.42461599644771203, 0.9033982135739806]
+| [https://dlmf.nist.gov/19.6#Ex26 19.6#Ex26] || <math qid="Q6170">\incellintPik@{\phi}{1}{1} = \tfrac{1}{2}(\CarlsonellintRC@{c}{c-1}+\sqrt{c}(c-1)^{-1})</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintPik@{\phi}{1}{1} = \tfrac{1}{2}(\CarlsonellintRC@{c}{c-1}+\sqrt{c}(c-1)^{-1})</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticPi[1, \[Phi],(1)^2] == Divide[1,2]*(1/Sqrt[c - 1]*Hypergeometric2F1[1/2,1/2,3/2,1-(c)/(c - 1)]+Sqrt[c]*(c - 1)^(- 1))</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [60 / 60]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.42461599644771203, 0.9033982135739806]
 Test Values: {Rule[c, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.19222674503116347, 1.0138365568937844]
 Test Values: {Rule[c, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/19.6#Ex27 19.6#Ex27] || [[Item:Q6171|<math>\incellintPik@{\phi}{0}{k} = \incellintFk@{\phi}{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintPik@{\phi}{0}{k} = \incellintFk@{\phi}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticPi(sin(phi), 0, k) = EllipticF(sin(phi), k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticPi[0, \[Phi],(k)^2] == EllipticF[\[Phi], (k)^2]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 30]
+| [https://dlmf.nist.gov/19.6#Ex27 19.6#Ex27] || <math qid="Q6171">\incellintPik@{\phi}{0}{k} = \incellintFk@{\phi}{k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintPik@{\phi}{0}{k} = \incellintFk@{\phi}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticPi(sin(phi), 0, k) = EllipticF(sin(phi), k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticPi[0, \[Phi],(k)^2] == EllipticF[\[Phi], (k)^2]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 30]
 |-
-| [https://dlmf.nist.gov/19.6#Ex28 19.6#Ex28] || [[Item:Q6172|<math>\incellintPik@{\phi}{k^{2}}{k} = \frac{1}{{k^{\prime}}^{2}}\left(\incellintEk@{\phi}{k}-\frac{k^{2}}{\Delta}\sin@@{\phi}\cos@@{\phi}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintPik@{\phi}{k^{2}}{k} = \frac{1}{{k^{\prime}}^{2}}\left(\incellintEk@{\phi}{k}-\frac{k^{2}}{\Delta}\sin@@{\phi}\cos@@{\phi}\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticPi(sin(phi), (k)^(2), k) = (1)/(1 - (k)^(2))*(EllipticE(sin(phi), k)-((k)^(2))/(Delta)*sin(phi)*cos(phi))</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticPi[(k)^(2), \[Phi],(k)^2] == Divide[1,1 - (k)^(2)]*(EllipticE[\[Phi], (k)^2]-Divide[(k)^(2),\[CapitalDelta]]*Sin[\[Phi]]*Cos[\[Phi]])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(infinity)+Float(infinity)*I
+| [https://dlmf.nist.gov/19.6#Ex28 19.6#Ex28] || <math qid="Q6172">\incellintPik@{\phi}{k^{2}}{k} = \frac{1}{{k^{\prime}}^{2}}\left(\incellintEk@{\phi}{k}-\frac{k^{2}}{\Delta}\sin@@{\phi}\cos@@{\phi}\right)</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintPik@{\phi}{k^{2}}{k} = \frac{1}{{k^{\prime}}^{2}}\left(\incellintEk@{\phi}{k}-\frac{k^{2}}{\Delta}\sin@@{\phi}\cos@@{\phi}\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticPi(sin(phi), (k)^(2), k) = (1)/(1 - (k)^(2))*(EllipticE(sin(phi), k)-((k)^(2))/(Delta)*sin(phi)*cos(phi))</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticPi[(k)^(2), \[Phi],(k)^2] == Divide[1,1 - (k)^(2)]*(EllipticE[\[Phi], (k)^2]-Divide[(k)^(2),\[CapitalDelta]]*Sin[\[Phi]]*Cos[\[Phi]])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(infinity)+Float(infinity)*I
 Test Values: {Delta = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.4574406724+1.116997071*I
 Test Values: {Delta = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
@@ Line 115: / Line 115: @@
 Test Values: {Rule[k, 2], Rule[Δ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/19.6#Ex29 19.6#Ex29] || [[Item:Q6173|<math>\incellintPik@{\phi}{1}{k} = \incellintFk@{\phi}{k}-\frac{1}{{k^{\prime}}^{2}}(\incellintEk@{\phi}{k}-\Delta\tan@@{\phi})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintPik@{\phi}{1}{k} = \incellintFk@{\phi}{k}-\frac{1}{{k^{\prime}}^{2}}(\incellintEk@{\phi}{k}-\Delta\tan@@{\phi})</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticPi(sin(phi), 1, k) = EllipticF(sin(phi), k)-(1)/(1 - (k)^(2))*(EllipticE(sin(phi), k)- Delta*tan(phi))</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticPi[1, \[Phi],(k)^2] == EllipticF[\[Phi], (k)^2]-Divide[1,1 - (k)^(2)]*(EllipticE[\[Phi], (k)^2]- \[CapitalDelta]*Tan[\[Phi]])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(infinity)+Float(infinity)*I
+| [https://dlmf.nist.gov/19.6#Ex29 19.6#Ex29] || <math qid="Q6173">\incellintPik@{\phi}{1}{k} = \incellintFk@{\phi}{k}-\frac{1}{{k^{\prime}}^{2}}(\incellintEk@{\phi}{k}-\Delta\tan@@{\phi})</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintPik@{\phi}{1}{k} = \incellintFk@{\phi}{k}-\frac{1}{{k^{\prime}}^{2}}(\incellintEk@{\phi}{k}-\Delta\tan@@{\phi})</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticPi(sin(phi), 1, k) = EllipticF(sin(phi), k)-(1)/(1 - (k)^(2))*(EllipticE(sin(phi), k)- Delta*tan(phi))</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticPi[1, \[Phi],(k)^2] == EllipticF[\[Phi], (k)^2]-Divide[1,1 - (k)^(2)]*(EllipticE[\[Phi], (k)^2]- \[CapitalDelta]*Tan[\[Phi]])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(infinity)+Float(infinity)*I
 Test Values: {Delta = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.5381374542+.4861981155*I
 Test Values: {Delta = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
@@ Line 121: / Line 121: @@
 Test Values: {Rule[k, 2], Rule[Δ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/19.6#Ex30 19.6#Ex30] || [[Item:Q6174|<math>\incellintPik@{\tfrac{1}{2}\pi}{\alpha^{2}}{k} = \compellintPik@{\alpha^{2}}{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintPik@{\tfrac{1}{2}\pi}{\alpha^{2}}{k} = \compellintPik@{\alpha^{2}}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticPi(sin((1)/(2)*Pi), (alpha)^(2), k) = EllipticPi((alpha)^(2), k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticPi[\[Alpha]^(2), Divide[1,2]*Pi,(k)^2] == EllipticPi[\[Alpha]^(2), (k)^2]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 9]
+| [https://dlmf.nist.gov/19.6#Ex30 19.6#Ex30] || <math qid="Q6174">\incellintPik@{\tfrac{1}{2}\pi}{\alpha^{2}}{k} = \compellintPik@{\alpha^{2}}{k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incellintPik@{\tfrac{1}{2}\pi}{\alpha^{2}}{k} = \compellintPik@{\alpha^{2}}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>EllipticPi(sin((1)/(2)*Pi), (alpha)^(2), k) = EllipticPi((alpha)^(2), k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticPi[\[Alpha]^(2), Divide[1,2]*Pi,(k)^2] == EllipticPi[\[Alpha]^(2), (k)^2]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 9]
 |-
-| [https://dlmf.nist.gov/19.6#Ex31 19.6#Ex31] || [[Item:Q6175|<math>\lim_{\phi\to 0}\ifrac{\incellintPik@{\phi}{\alpha^{2}}{k}}{\phi} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\lim_{\phi\to 0}\ifrac{\incellintPik@{\phi}{\alpha^{2}}{k}}{\phi} = 1</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>limit((EllipticPi(sin(phi), (alpha)^(2), k))/(phi), phi = 0) = 1</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[Divide[EllipticPi[\[Alpha]^(2), \[Phi],(k)^2],\[Phi]], \[Phi] -> 0, GenerateConditions->None] == 1</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 9]
+| [https://dlmf.nist.gov/19.6#Ex31 19.6#Ex31] || <math qid="Q6175">\lim_{\phi\to 0}\ifrac{\incellintPik@{\phi}{\alpha^{2}}{k}}{\phi} = 1</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\lim_{\phi\to 0}\ifrac{\incellintPik@{\phi}{\alpha^{2}}{k}}{\phi} = 1</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>limit((EllipticPi(sin(phi), (alpha)^(2), k))/(phi), phi = 0) = 1</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[Divide[EllipticPi[\[Alpha]^(2), \[Phi],(k)^2],\[Phi]], \[Phi] -> 0, GenerateConditions->None] == 1</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 9]
 |-
-| [https://dlmf.nist.gov/19.6#Ex32 19.6#Ex32] || [[Item:Q6176|<math>\CarlsonellintRC@{x}{x} = x^{-1/2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\CarlsonellintRC@{x}{x} = x^{-1/2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>1/Sqrt[x]*Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(x)] == (x)^(- 1/2)</syntaxhighlight> || Missing Macro Error || Successful || - || Successful [Tested: 3]
+| [https://dlmf.nist.gov/19.6#Ex32 19.6#Ex32] || <math qid="Q6176">\CarlsonellintRC@{x}{x} = x^{-1/2}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\CarlsonellintRC@{x}{x} = x^{-1/2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>1/Sqrt[x]*Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(x)] == (x)^(- 1/2)</syntaxhighlight> || Missing Macro Error || Successful || - || Successful [Tested: 3]
 |-
-| [https://dlmf.nist.gov/19.6#Ex33 19.6#Ex33] || [[Item:Q6177|<math>\CarlsonellintRC@{\lambda x}{\lambda y} = \lambda^{-1/2}\CarlsonellintRC@{x}{y}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\CarlsonellintRC@{\lambda x}{\lambda y} = \lambda^{-1/2}\CarlsonellintRC@{x}{y}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>1/Sqrt[\[Lambda]*y]*Hypergeometric2F1[1/2,1/2,3/2,1-(\[Lambda]*x)/(\[Lambda]*y)] == \[Lambda]^(- 1/2)* 1/Sqrt[y]*Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(y)]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [75 / 180]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[2.0541315094196904, 2.1051836996148214]
+| [https://dlmf.nist.gov/19.6#Ex33 19.6#Ex33] || <math qid="Q6177">\CarlsonellintRC@{\lambda x}{\lambda y} = \lambda^{-1/2}\CarlsonellintRC@{x}{y}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\CarlsonellintRC@{\lambda x}{\lambda y} = \lambda^{-1/2}\CarlsonellintRC@{x}{y}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>1/Sqrt[\[Lambda]*y]*Hypergeometric2F1[1/2,1/2,3/2,1-(\[Lambda]*x)/(\[Lambda]*y)] == \[Lambda]^(- 1/2)* 1/Sqrt[y]*Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(y)]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [75 / 180]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[2.0541315094196904, 2.1051836996148214]
 Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[2.941079989400646, 0.036099349881403064]
 Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/19.6#Ex35 19.6#Ex35] || [[Item:Q6179|<math>\CarlsonellintRC@{0}{y} = \tfrac{1}{2}\pi y^{-1/2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\CarlsonellintRC@{0}{y} = \tfrac{1}{2}\pi y^{-1/2}</syntaxhighlight> || <math>|\phase@@{y}| < \pi</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>1/Sqrt[y]*Hypergeometric2F1[1/2,1/2,3/2,1-(0)/(y)] == Divide[1,2]*Pi*(y)^(- 1/2)</syntaxhighlight> || Missing Macro Error || Successful || - || Successful [Tested: 3]
+| [https://dlmf.nist.gov/19.6#Ex35 19.6#Ex35] || <math qid="Q6179">\CarlsonellintRC@{0}{y} = \tfrac{1}{2}\pi y^{-1/2}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\CarlsonellintRC@{0}{y} = \tfrac{1}{2}\pi y^{-1/2}</syntaxhighlight> || <math>|\phase@@{y}| < \pi</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>1/Sqrt[y]*Hypergeometric2F1[1/2,1/2,3/2,1-(0)/(y)] == Divide[1,2]*Pi*(y)^(- 1/2)</syntaxhighlight> || Missing Macro Error || Successful || - || Successful [Tested: 3]
 |-
-| [https://dlmf.nist.gov/19.6#Ex36 19.6#Ex36] || [[Item:Q6180|<math>\CarlsonellintRC@{0}{y} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\CarlsonellintRC@{0}{y} = 0</syntaxhighlight> || <math>y < 0</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>1/Sqrt[y]*Hypergeometric2F1[1/2,1/2,3/2,1-(0)/(y)] == 0</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.0, -1.2825498301618643]
+| [https://dlmf.nist.gov/19.6#Ex36 19.6#Ex36] || <math qid="Q6180">\CarlsonellintRC@{0}{y} = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\CarlsonellintRC@{0}{y} = 0</syntaxhighlight> || <math>y < 0</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>1/Sqrt[y]*Hypergeometric2F1[1/2,1/2,3/2,1-(0)/(y)] == 0</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.0, -1.2825498301618643]
 Test Values: {Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.0, -2.221441469079183]
 Test Values: {Rule[y, -0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |}
 </div>

19.6: Difference between revisions

Latest revision as of 11:49, 28 June 2021

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